## Calculus with Applications (10th Edition)

Published by Pearson

# Chapter R - Algebra Reference - R.1 Polynomials - R.2 Exercises - Page R-7: 4

#### Answer

$$10m^2(6m-n)(m-5n)$$

#### Work Step by Step

Factor out the greatest common factor from all the terms in the expression, in this case, $10m^2$, $$60m^4-120m^3n+50m^2n^2=10m^2(6m^2-12mn+5n^2)$$ Next factor the trinomial. The possible factors of $6m^2$ are $6m$ and $m$ or $3m$ and $2m$. The possible factors of $5n^2$ are $5n$ and $n$. Test different combinations to find the set that works. $$=10m^2(6m-n)(m-5n)$$

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